The truce was reportedly brokered by US President Barack Obama in the dying hours of his three-day visit to Israel and Palestine – Mr Netanyahu make the phone call in a trailer on the tarmac at Ben Gurion airport just before Mr Obama flew to Jordan.

The US president joined the phone conversation at one point, a US official quoted in the Haaretz newspaper said.

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Turkey has long demanded an apology from Israel for the raid on the flotilla’s lead ship, the Mavi Marmara, on May 31 2010 in which Israeli naval commandos boarded the ship in international waters in order to prevent it from breaching Israel's naval blockade and reaching Gaza.

Nine Turkish activists were killed in the raid, prompting worldwide condemnation of Israel’s actions. Turkey cut all diplomatic ties with Israel in response, expelling Israel’s ambassador and freezing all military cooperation with Ankara.

Soon after Israel eased its blockade of Gaza, although it still imposes significant restrictions on the import and export of goods, the travel on Gazans through Israel into the West Bank, on farmers working lands on the border and on fishermen off the Mediterranean coast.

“Prime Minister Netanyahu apologised to the Turkish people for any mistakes that might have led to loss of life or injury and agreed to conclude an agreement on compensation,” a statement from Mr Netanyahu’s office read last night.

President Obama welcomed the move, saying in statement released soon after he left Israel that “we attach great importance to the restoration of positive relations between them in order to advance regional peace and security”.

“I am hopeful that today's exchange between the two leaders will enable them to engage in deeper cooperation on this and a range of other challenges and opportunities,” the US President said.

During the phone call Mr Netanyahu expressed regret to Mr Erdogan over the deterioration in bilateral relations between Israel and Turkey and said he was committed to “working out the disagreements in order to advance peace and regional stability”.

“The Prime Minister made it clear that the tragic results regarding the Mavi Marmara were unintentional and that Israel expresses regret over injuries and loss of life,” the statement said, noting that an Israeli investigation into the incident had found “several operational errors”.

Last year a Turkish court began hearing murder charges against four former high-ranking Israeli military officials who oversaw the raid on the Mavi Marmara.

A United Nations inquiry into the incident found Israel's naval blockade was justified, but said the soldiers had used “excessive and unreasonable” force in the raid.

“We welcome Israel's apology. This is a major victory for diplomacy,” Ibrahim Kalin, chief advisor to Mr Erdogan and a fellow at the Prince Alwaleed Center for Muslim-Christian Understanding at Georgetown University tweeted overnight.